The invention relates to a method for use in the correction of non-linearity and noise in the conversion of a PCM signal into a UPWM signal.
Such a conversion of a digital signal into a pulse width modulated signal may advantageously be used in connection with power amplifiers which are of the class D type. In connection with digital sound sources, such as compact disc players, where the sound signals are pulse code modulated, a conversion of the pulse code modulation into pulse width modulation will make it extremely suitable for the connection of a class D amplifier. The class D amplifier primarily has the advantage that it has a very high efficiency, which means that it may be constructed with a low weight while maintaining an extremely high output power, it being possible to achieve an efficiency of almost 95% for a class D amplifier. Further, connection of a digital sound source and a class D amplifier will allow analog signal processing to be avoided, which is an advantage in the signal processing.
Thus, it is desirable to be able to convert a pulse code modulated signal into a pulse width modulated signal without the information in the pulse code modulating signal being changed in the conversion.
It has been known for many years that the conversion of a pulse code modulation signal into a pulse width, modulated signal is non-linear by nature.
Several methods have been proposed in the course of time for the correction of this non-linearity, which is fundamentally necessary if a digital sound source, such as a compact disc player, is to be used in connection with an amplifier to which a pulse width modulated signal is fed as an input signal.
In addition to the inevitable non-linearity, the conversion of the pulse code modulation signal into the pulse width modulation signal generates noise which also has to be corrected if the orignal information from a digital sound source is to be reproduced correctly.
This noise occurs since the PWM signal is desirably formed as a digital signal, which means that all level switchings take place synchronously with a bit clock which has a limited frequency. Thus, the UPWM signal must be capable of being formed by a digital circuit which gives rise to a coarse quantization and thereby noise.
Examples of methods for the elimination of error sources which occur if a pulse code modulation signal is converted into a pulse width modulated signal include:
Use of oversampling, which means that the switching frequency is considerably greater than is necessary according to the sampling theorem in the generation of the pulse width modulated signal which is used in the pulse code modulation. However, too strong oversampling is not desirable in practical uses, because this inevitably creates noise. Problems will primarily occur with a class D output stage which is to switch correspondingly rapidly.
Although, as mentioned above, the noise, also called quantization noise, can be reduced using so-called noise shaping, where the quantization noise at high frequencies is amplified, while the noise from the lower frequencies is removed, but the interaction of the quantization noise with the non-linear pulse width modulation gives rise to so-called intermodulation noise, causing a new error source called intermodulation noise (IM noise) to be generated by noise shaping, which means that the advantageous effect of the noise shaping is reduced.
The published international patent application No. WO 92/15153 discloses a method of correcting non-linearity and correcting deterministic distortion as well as intermodulation noise. The document describes a plurality of complex circuits including look-up tables, used for the determination of parameters, for use in the feedback to suppress the deterministic distortion and the intermodulation noise. In practice, however, it is necessary to use look-up tables of a considerable extent, which will hardly be easy to implement, in connection with pulse code modulation signals of 16-24 bits.
The published international patent application No. WO 92/11699 discloses an equalization method based on an imitation of the naturally sampled PWM. The method has no effect on the inevitably occurring intermodulation noise as well as possible. noise which is generated if a so-called quasi-symmetrical uniform pulse width modulation is used. Further, the method cannot be applied in connection with all UPWM forms (e.g. double-sided, symmetrical).
As a starting point for the invention it is desired to provide a new and better method of modelling, and thereby also predicting, the non-linearity of a pulse code modulation to a pulse width modulation conversion process.
As will appear from the following, it has been found that the use of so-called Hammerstein filters, which generally consist of a static non-linearity followed by a linear, time invariant filter, is extremely suitable for the correction of several of the error sources which occur in pulse code modulation to pulse width modulation.
Of these error sources, in particular the following four ones are interesting in connection with the present invention:
1. Quantization noise because of the time discretization of pulse width information.
2. Intermodulation noise which is created by the uniform pulse width modulation because of quantization and noise shaping.
3. Noise because of the use of quasi-symmetrical uniform pulse width modulation.
4. Deterministic harmonic distortion.
Thus, it is desirable to provide some correction circuits which each are directed to the above-mentioned error sources 1-4.
As will appear from the following, the error sources 1-3 will be corrected by simple feedback circuits, while the error source 4 will be corrected by signal feedforward.
The object of the invention is to provide a method for use in the correction of the errors which occur in the conversion of pulse code modulation into a pulse width modulation, thereby minimizing non-linearities and noise which inevitably occur in connection therewith.
The object is achieved by designing a model circuit for the known non-linearity in the PCM to UPWM conversion, said model circuit being formed by parallel-connected Hammerstein filters which divide the PCM signal into their respective polynomial components, each of said polynomial components being filtered with a linear and time invariant filter associated with the power l and having the transfer function:                     A        l            ⁡              (        z        )              =                  ∑        i            ⁢              xe2x80x83            ⁢                        a          il                ⁢                  z          i                      ,
where z=ejxcfx89
following which the filtered components are summed, with z=ejxcfx89, where xcfx89=2xcfx80f/fs represents the normalized angle frequency and fs is the sampling frequency and ai1 represents the filter coefficient associated with the power 1 and time index 1.
This ensures that the non-linearity in the pulse code modulation to pulse width modulation may be modelled, without complicated table-based memories having to be used. Thus, instead, use is made of a method which may be implemented by simple circuits consisting of Hammerstein filters.
It is expedient that the non-linear polynomial components are determined by a Taylor development of the pulse code modulation signal.
It is expedient that in a UPWM trailing edge modulation the coefficients of the filters are determined so as to achieve the following transfer functions:             A      l        ⁡          (      ω      )        =            1              l        !              ⁢                  (                                            -              j                        ⁢                          xe2x80x83                        ⁢            ω                    2                )                    (                  l          -          1                )            
It is expedient that in a UPWM leading edge modulation the coefficients of the filters are determined so as to achieve the following transfer functions:             A      l        ⁡          (      ω      )        =            1              l        !              ⁢                  (                              j            ⁢                          xe2x80x83                        ⁢            ω                    2                )                    (                  l          -          1                )            
According to the method, it is moreover expedient that in an UPWM double-sided symmetrical modulation the filter coefficients are determined so as to achieve the following transfer functions:             A      1        ⁡          (      ω      )        ≈      {                                                                      1                                  1                  !                                            ⁢                                                (                                                            j                      ⁢                                              xe2x80x83                                            ⁢                      ω                                        4                                    )                                                  (                                      l                    -                    1                                    )                                                      ,                          for              ⁢                              xe2x80x83                            ⁢              odd              ⁢                              xe2x80x83                            ⁢              1                                                                                                      1                                  1                  !                                            ⁢                                                (                                                            j                      ⁢                                              xe2x80x83                                            ⁢                      ω                                        4                                    )                                1                                      ,                          for              ⁢                              xe2x80x83                            ⁢              even              ⁢                              xe2x80x83                            ⁢              1                                          
It is noted that a more linear process is obtained when using double-sided symmetrical uniform pulse width modulation.
The invention also concerns a circuit for correcting non-linearity and noise in the conversion of a PCM signal into a UPWM signal.
This circuit is characterized in that the PCM signal is fed to a plurality of parallel-connected Hammerstein filters which divide the PCM signal into their respective polynomial components which each are filtered with a linear filter belonging to the power 1 and having the transfer function B1(xcfx89), adapted to equalize the non-linear contributions caused by the PCM-UPWM conversion, said B1(xcfx89) being approximated on the basis of the knowledge of the model circuit as previously disclosed herein, following which the filtered components are fed to a summation unit.
This provides a circuit which is simple to realize, and which is based exclusively on signal feedforward, which causes no problems of stability.
For optimum realization of the circuit, it is an advantage that a time delay circuit is inserted after the 1st order component.
To remove the noise which, as mentioned before, inevitably occurs in discretization of the PCM signal, it is expedient that the input of the noise shaper is associated with a summation unit which, in addition to receiving the PCM signal, is adapted to receive and subtract a feedback signal derived as the difference between the output signals of two UPWM models as previously disclosed herein, wherein the input signal to the first model, which is a first Hammerstein filter, is formed by the PCM signal, and the input signal to the second model, which is a second Hammerstein filter, is formed by the output signal of the noise shaper.
The PCM signal may be corrected in connection with the use of quasi-symmetrical modulation by feedback from a Hammerstein filter whose non-linear part is formed by a generator signal g(k), which, dynamically, is an indication of the selected symmetry form and pulse width for the modulated pulse associated with the time index k, and whose linear part is a time invariant filter having the transfer function C(xcfx89).
It is advantageous if the generator signal g(k) is given by:
g(k)=s(k)(x(k)+1)
where (x(k)+1) represents the width of the pulse at time index k and s(k) represents the time shift with respect to symmetrical modulation of the pulse at time index k expressed in half bit clock periods Tb, and where C(xcfx89) is approximated by the transfer function:       C    ⁡          (      ω      )        =      j    ⁢          xe2x80x83        ⁢    ω    ⁢                  T        b                    2        ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢        T            
where Tb is the cycle time of the bit clock, while xcex94T represents the cycle time of the UPWM signal.
Finally, the invention relates to use with a class D amplifier or equipment for digital-to-analog conversion.
The invention has the advantage that it allows construction of a digital amplifier in which analog calculation circuits are not used at any time.
As explained above, the invention thus provides circuits which are all based on Hammerstein filters which, as mentioned before, in principle consist of a non-linear circuit followed by a linear and time invariant filter. Thus by applying the principles of the method according to the invention it is possible to construct circuits capable of correcting non-linearities as well as noise, including intermodulation noise which inevitably occur in connection with digital signal processing. In short, it has now been made possible to construct purely digital amplifiers without analog signal processing and without using A/D, D/A converters.